Results for the regional assessment (PhD Chapter 1)

This series of files compile all analyses done during Chapter 1 for the regional assessment (Campaign 2016):

All analyses have been done with PRIMER-e 6 and R 3.6.0.

Caracteristics of each campaign

2014 2016 2017
Sampling date August-September June to August July
Criteria for perturbation Potentially impacted if close to the city or industries, References outside the bay Human-impacted if in a region with a highly populated area, industries and maritime activities, Reference if none of these criteria Human-impacted if in a region with a highly populated area, industries and maritime activities, Reference if none of these criteria
Regions considered BSI BSI, CPC, BDA, MR BSI, MR
Number of sampled stations 40 (20 HI, 20 R) 78 (26 BSI, 19 CPC, 18 BDA, 15 MR) 126 (111 BSI, 15 MR)
Parameters sampled Organic matter yes yes yes
Photosynthetic pigments no yes yes
Sediment grain-size yes yes yes
Heavy-metals yes yes (for a limited number of stations) no (interpolated based on 2014 and 2016 values)
Benthic communities Compartment targeted Macro-infauna Macro-infauna Macro-infauna
Sieved used 500 µm 1 mm 500 µm and 1 mm
Conservation technique Formaldehyle Formaldehyle Formaldehyle
Others N.A. N.A. N.A.

Click on the table of contents in the left margin to assess a specific analysis
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To assess Section 1, click here.
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We selected variables and characteristic species (using IndVal index and SIMPER procedure, see Section 2) for the analyses:

As there is missing data for metal concentrations outside BSI, two Designs have been used:

Workspace preparation

Here, we use data from subtidal ecosystems (see metadata files for more information)
Only stations that have been sampled both for abiotic parameters and benthic species were included.
The script below includes personnal functions, refined data, parameters for each campaign and global means, sd, se.

1. Permutational Analyses of Variance

Results of univariate PermANOVAs on parameters and multivariate PermANOVA on the whole benthic community are presented in the table below.

Variable Condition Region(Co) Significative groups of similar regions (p > 0.05)
depth All regions in the same group
om S (CPC BDA MR)
gravel All regions in the same group
sand All regions in the same group
silt (BSI CPC BDA), (BDA MR)
clay (BSI BDA MR), (CPC MR)
S (1 mm) (BSI CPC MR), (CPC BDA MR)
N (1 mm) All regions in the same group
H (1 mm) S (CPC BDA MR), (BSI MR)
J (1 mm) (BSI CPC MR), (CPC BDA MR)
Marc (1 mm) (BSI BDA MR), (BSI CPC MR)
Cgra (1 mm) (BSI CPC BDA), (BSI BDA MR)
ALL SPECIES (1 mm) S

2. IndVal and SIMPER

These analyses allowed to select species as dependant variables for the regressions. We used results from PRIMER to justify further their choice.

##                       cluster indicator_value probability
## cistenides_granulata        1          0.3080       0.018
## ennucula_tenuis             1          0.2222       0.006
## macoma_calcarea             1          0.2222       0.004
## eudorellopsis_integra       1          0.1556       0.038
## mesodesma_arctatum          2          0.2535       0.003
## harmothoe_imbricata         2          0.2008       0.005
## glycera_alba                2          0.1212       0.029
## psammonyx_nobilis           2          0.1212       0.036
## 
## Sum of probabilities                 =  51.022 
## 
## Sum of Indicator Values              =  6.08 
## 
## Sum of Significant Indicator Values  =  1.6 
## 
## Number of Significant Indicators     =  8 
## 
## Significant Indicator Distribution
## 
## 1 2 
## 4 4
SIMPER results (average dissimilarity: 94.67 )
  average sd ratio ava avb cumsum
echinarachnius_parma 0.131 0.205 0.638 4.18 1.33 0.138
mesodesma_arctatum 0.0987 0.205 0.482 3.52 0.267 0.242
cistenides_granulata 0.0671 0.128 0.525 0.485 1.62 0.313
strongylocentrotus_sp 0.0438 0.108 0.404 0.667 0.867 0.36
nephtys_caeca 0.034 0.0584 0.581 0.636 0.667 0.395
protomedeia_grandimana 0.0329 0.0819 0.402 0.636 0.933 0.43
scoloplos_armiger 0.0317 0.0798 0.397 1.06 1.11 0.464
amphipholis_squamata 0.0306 0.119 0.257 0.0606 2.96 0.496
limecola_balthica 0.0266 0.0543 0.49 0.606 0.489 0.524
macoma_calcarea 0.0241 0.0588 0.41 0 0.733 0.549
thyasira_sp 0.0233 0.0613 0.38 0.0303 0.933 0.574
ennucula_tenuis 0.0225 0.0545 0.413 0 1.02 0.598
psammonyx_nobilis 0.0203 0.0744 0.273 0.515 0 0.619
harmothoe_imbricata 0.0193 0.052 0.372 0.394 0.0222 0.64
pygospio_elegans 0.0193 0.0996 0.193 2.76 0.0222 0.66
pontoporeia_femorata 0.0151 0.0727 0.208 0 0.733 0.676
glycera_alba 0.0142 0.0566 0.25 0.515 0 0.691
ameritella_agilis 0.0141 0.0687 0.206 0 0.444 0.706
astarte_undata 0.014 0.0482 0.29 0.364 0.0222 0.721
ciliatocardium_ciliatum 0.0136 0.0497 0.273 0.182 0.222 0.735
astarte_subaequilatera 0.013 0.0485 0.268 0.364 0 0.749
bipalponephtys_neotena 0.0122 0.0715 0.17 0 0.556 0.762
mya_arenaria 0.0114 0.0264 0.433 0.0909 0.311 0.774
goniada_maculata 0.0109 0.0382 0.286 0.0303 0.333 0.785
ampharete_oculata 0.0104 0.0649 0.16 0.242 0 0.796
nucula_proxima 0.0096 0.0398 0.241 0 0.244 0.806
glycera_dibranchiata 0.00933 0.0351 0.266 0.0303 0.133 0.816
diastylis_sculpta 0.00903 0.0473 0.191 0.121 0.0444 0.826
testudinalia_testudinalis 0.00864 0.0382 0.226 0.212 0.0444 0.835
ampharetidae_spp 0.0069 0.0212 0.326 0.121 0.111 0.842
eudorellopsis_integra 0.00677 0.0217 0.312 0 0.333 0.849
maldanidae_spp 0.00645 0.0231 0.279 0.212 0.0444 0.856
ampeliscidae_spp 0.00641 0.0199 0.322 0.0909 0.0889 0.863
yoldia_myalis 0.00622 0.0215 0.289 0.0909 0.0667 0.87
nephtys_ciliata 0.00618 0.0252 0.245 0 0.2 0.876
ophelia_limacina 0.00592 0.0203 0.292 0.0606 0.0889 0.882
phyllodoce_mucosa 0.00572 0.0232 0.247 0 0.333 0.888
polynoidae_spp 0.00571 0.0156 0.366 0.0303 0.222 0.894

3. Univariate regressions

Independant variables are habitat parameters and heavy metal concentrations, dependant variables are diversity indices and characteristic species abundances.

i) Identification of outliers

To identify stations that are not consistent with the others, we used the multivariate Cook’s Distance (CD) on the uncorrelated variables. A significative threshold of 4 times the mean of CD has been established.
We used linear models for the regressions on diversity indices, and generalized linear models with Poisson distribution for species abundances.

Design 1

Based on Cook’s Distance, we identified stations 74, 80, 87, 107, 111 and 126 as general outliers. They have been deleted for the following analyses of Design 1.

Design 2

Based on Cook’s Distance, we identified stations 104, 108 and 110 as general outliers. They have been deleted for the following analyses of Design 2.

ii) Correlations between parameters

Correlations have been calculated with Spearman’s rank coefficient.

Design 1

Correlation coefficients between habitat parameters (Design 1)
  depth om gravel sand silt clay
depth 1 0.498 0.112 -0.514 0.418 0.431
om 0.498 1 -0.075 -0.814 0.731 0.722
gravel 0.112 -0.075 1 -0.168 -0.385 -0.333
sand -0.514 -0.814 -0.168 1 -0.781 -0.79
silt 0.418 0.731 -0.385 -0.781 1 0.97
clay 0.431 0.722 -0.333 -0.79 0.97 1

According to these results, the following variables are highly correlated so they have been considered together in the regressions (\(|\rho|\) > 0.80):

  • om and sand (sand deleted)
  • silt and clay (clay deleted)

Design 2

Correlation coefficients between habitat parameters and metals concentrations (Design 2)
  depth om gravel sand silt clay arsenic cadmium chromium copper iron manganese mercury lead zinc
depth 1 0.538 -0.309 -0.341 0.45 0.465 0.483 -0.069 0.3 0.424 0.332 -0.086 0.511 0.384 0.471
om 0.538 1 -0.606 -0.746 0.868 0.881 0.798 0.449 0.653 0.894 0.557 0.314 0.698 0.833 0.863
gravel -0.309 -0.606 1 0.166 -0.699 -0.677 -0.374 -0.544 -0.344 -0.545 -0.308 -0.352 -0.134 -0.456 -0.596
sand -0.341 -0.746 0.166 1 -0.786 -0.782 -0.636 -0.355 -0.684 -0.715 -0.527 -0.341 -0.554 -0.765 -0.699
silt 0.45 0.868 -0.699 -0.786 1 0.98 0.685 0.551 0.685 0.8 0.56 0.441 0.467 0.799 0.835
clay 0.465 0.881 -0.677 -0.782 0.98 1 0.704 0.512 0.702 0.828 0.555 0.401 0.506 0.814 0.856
arsenic 0.483 0.798 -0.374 -0.636 0.685 0.704 1 0.411 0.657 0.862 0.721 0.349 0.575 0.794 0.847
cadmium -0.069 0.449 -0.544 -0.355 0.551 0.512 0.411 1 0.723 0.411 0.709 0.836 0.083 0.602 0.658
chromium 0.3 0.653 -0.344 -0.684 0.685 0.702 0.657 0.723 1 0.637 0.8 0.767 0.42 0.752 0.85
copper 0.424 0.894 -0.545 -0.715 0.8 0.828 0.862 0.411 0.637 1 0.546 0.286 0.51 0.832 0.861
iron 0.332 0.557 -0.308 -0.527 0.56 0.555 0.721 0.709 0.8 0.546 1 0.739 0.391 0.623 0.814
manganese -0.086 0.314 -0.352 -0.341 0.441 0.401 0.349 0.836 0.767 0.286 0.739 1 0.09 0.499 0.578
mercury 0.511 0.698 -0.134 -0.554 0.467 0.506 0.575 0.083 0.42 0.51 0.391 0.09 1 0.559 0.492
lead 0.384 0.833 -0.456 -0.765 0.799 0.814 0.794 0.602 0.752 0.832 0.623 0.499 0.559 1 0.821
zinc 0.471 0.863 -0.596 -0.699 0.835 0.856 0.847 0.658 0.85 0.861 0.814 0.578 0.492 0.821 1

According to these results, the following variables are highly correlated so they have been considered together in the regressions (\(|\rho|\) > 0.80):

  • om and copper (copper deleted)
  • silt and clay (clay deleted)
  • lead and zinc (zinc deleted)

We also decided to exclude sand content in the regressions, as it tends to increase drasticaly VIFs due to a marginal negative correlation with silt and clay.

iii) Simple regressions

These analyses have been do to explore the relationships between variables. As it is a huge number of results to interpret, only multiple regressions will be included in the article (see below).

Design 1

Adjusted R-squared of simple regressions for Design 1
  depth om gravel silt
S 0.1745 0.08189 0.01292 0.1223
N -0.005956 0.01079 0.002965 0.02872
H 0.2179 0.08459 -0.01115 0.1075
J 0.02881 0.001654 0.006298 0.01015
Marc 0.02454 -0.01282 -0.007057 -0.008682
Cgra 0.00757 -0.0121 -0.01174 -0.01398
p-values of simple regressions for Design 1
  depth om gravel silt
S 0.0001546 0.008504 0.1692 0.001523
N 0.449 0.1872 0.2749 0.0827
H 2.13e-05 0.007585 0.6429 0.002865
J 0.08235 0.2941 0.2326 0.1929
Marc 0.09955 0.7512 0.4808 0.5349
Cgra 0.2185 0.6983 0.676 0.8853

Design 2

Adjusted R-squared of simple regressions for Design 2
  depth om gravel silt arsenic cadmium chromium iron manganese mercury lead
S 0.2707 0.03698 0.1377 0.1268 -0.02305 -0.04725 -0.02327 -0.04316 -0.04679 -0.04713 0.102
N 0.09012 0.06662 0.148 0.1598 0.009787 -0.02218 0.009648 -0.02519 -0.04584 -0.04743 0.1177
H 0.3677 0.0403 0.1874 0.1195 -0.03075 -0.04719 -0.02167 -0.03706 -0.04762 -0.02843 0.08102
J 0.0211 -0.04663 0.002418 -0.04554 -0.04376 -0.03974 -0.04241 -0.04181 -0.03541 -0.03347 -0.04581
Marc -0.01444 -0.02484 -0.0277 -0.001265 -0.01935 0.08445 0.0811 0.04514 -0.00923 -0.01731 0.06695
Cgra -0.04616 -0.04259 -0.03938 -0.04446 -0.04717 0.03627 0.02581 -0.01584 0.01732 -0.0205 -0.02944
p-values of simple regressions for Design 2
  depth om gravel silt arsenic cadmium chromium iron manganese mercury lead
S 0.006407 0.1888 0.04566 0.05328 0.4854 0.9324 0.4874 0.7675 0.8984 0.9222 0.07545
N 0.08905 0.1238 0.03946 0.03336 0.2823 0.4777 0.2829 0.5053 0.8519 0.9519 0.06052
H 0.001285 0.18 0.02243 0.05903 0.564 0.927 0.4733 0.6485 0.9941 0.5381 0.1012
J 0.2382 0.8892 0.3164 0.8399 0.7832 0.694 0.7491 0.7355 0.6239 0.5975 0.8506
Marc 0.4166 0.5019 0.5304 0.3354 0.4539 0.09641 0.101 0.1679 0.3816 0.4378 0.1233
Cgra 0.8656 0.7535 0.6875 0.8033 0.9253 0.1908 0.2222 0.4267 0.252 0.4633 0.5491

iv) Multiple regressions

This section presents analyses done (i) to determine which model (Design 1, Design 2 metals, parameters or all) decribes the best the parameters and (ii) which variables are the most important to explain the parameters.
We used linear models for the regressions on diversity indices, and generalized linear models with Poisson distribution for species abundances. We also used ZIP models, but they are “computationally” singular, so they have not been computed here.

A. Best model selection

The aim is to descriminate the effect of habitat parameters and heavy metal concentrations on the dependant variables.

Results of the model selection are summurized below (according to AIC).

Model S N H J Marc Cgra
Design 1 341.7 679.1 111.4 17.11 538.9 325.6
Design 2 116 211.8 33.57 4.742 30.93 86.1
Metals Design 2 119.8 208.6 41.85 7.091 22.93 84.73
Parameters Design 2 114.9 202.7 27.2 1.246 40.16 118.3

Species richness

  n df AIC ∆AIC R2adj
Parameters 23 6 114.9 0 0.34
Design 2 23 13 116 1.112 0.38
Metals 23 9 119.8 4.979 0.24
Design 1 72 6 341.7 226.8 0.23

Total abundance

  n df AIC ∆AIC R2adj
Parameters 23 6 202.7 0 0.2
Metals 23 9 208.6 5.925 0.04
Design 2 23 13 211.8 9.182 -0.07
Design 1 72 6 679.1 476.5 0

Shannon index

  n df AIC ∆AIC R2adj
Parameters 23 6 27.2 0 0.46
Design 2 23 13 33.57 6.374 0.37
Metals 23 9 41.85 14.65 0.06
Design 1 72 6 111.4 84.21 0.23

Piélou’s evenness

  n df AIC ∆AIC R2adj
Parameters 23 6 1.246 0 -0.09
Design 2 23 13 4.742 3.496 -0.13
Metals 23 9 7.091 5.845 -0.3
Design 1 72 6 17.11 15.86 0.02

Abundance of M. arctatum

  n df AIC ∆AIC Pseudo-R2
Metals 23 8 22.93 0 0.89
Design 2 23 12 30.93 8 0.89
Parameters 23 5 40.16 17.23 0.52
Design 1 72 5 538.9 515.9 0.15

Abundance of C. granulata

  n df AIC ∆AIC Pseudo-R2
Metals 23 8 84.73 0 0.38
Design 2 23 12 86.1 1.376 0.44
Parameters 23 5 118.3 33.6 0.03
Design 1 72 5 325.6 240.9 0.04

B. Significative variables selection

We identified which variables are selected after an AIC procedure to best predict the variation of the parameters.

Design 1

Results of the variables selection are summurized below (according to AIC).

Variable S N H J Marc Cgra
depth + + + - +
om + + -
gravel - - -
silt + + -
Adjusted-R2 0.23 0.03 0.24 0.03
McFadden Pseudo-R2 0.15 0.04
Species richness
## FULL MODEL
## Adjusted R2 is: 0.23
Fitting linear model: S ~ depth + om + gravel + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.219 0.5006 6.429 1.568e-08 * * *
depth 0.06122 0.01816 3.371 0.001246 * *
om 0.3404 0.6623 0.5139 0.609
gravel -4.544 2.726 -1.667 0.1003
silt 1.228 1.823 0.6735 0.5029
Variance Inflation Factors
  depth om gravel silt
VIF 1.09 1.7 1.07 1.79 
## REDUCED MODEL
## Adjusted R2 is: 0.23
Fitting linear model: S ~ depth + gravel + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.298 0.4735 6.965 1.637e-09 * * *
depth 0.06111 0.01806 3.383 0.001191 * *
gravel -4.221 2.639 -1.6 0.1143
silt 1.966 1.116 1.762 0.08261
Variance Inflation Factors
  depth gravel silt
VIF 1.09 1.04 1.1 
## Analysis of Variance Table
## 
## Model 1: S ~ depth + om + gravel + silt
## Model 2: S ~ depth + gravel + silt
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     67 410.67                           
## 2     68 412.28 -1   -1.6187 0.2641  0.609
## RMSE for the full model: 2.572091
## RMSE for the reduced model: 2.500579

Total abundance
## FULL MODEL
## Adjusted R2 is: 0
Fitting linear model: N ~ depth + om + gravel + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.99 5.214 3.067 0.003119 * *
depth 0.06425 0.1891 0.3397 0.7351
om 0.6372 6.898 0.09238 0.9267
gravel -23.73 28.39 -0.8356 0.4063
silt 13.9 18.99 0.7319 0.4668
Variance Inflation Factors
  depth om gravel silt
VIF 1.09 1.7 1.07 1.79 
## REDUCED MODEL
## Adjusted R2 is: 0.03
Fitting linear model: N ~ silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.92 3.641 4.374 4.16e-05 * * *
silt 18.38 10.44 1.76 0.0827
Variance Inflation Factors
  silt
VIF 1 
## Analysis of Variance Table
## 
## Model 1: N ~ depth + om + gravel + silt
## Model 2: N ~ silt
##   Res.Df   RSS Df Sum of Sq      F Pr(>F)
## 1     67 44541                           
## 2     70 45032 -3   -490.72 0.2461 0.8639
## RMSE for the full model: 27.01001
## RMSE for the reduced model: 25.83092

Shannon index
## FULL MODEL
## Adjusted R2 is: 0.23
Fitting linear model: H ~ depth + om + gravel + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7352 0.1012 7.268 5.015e-10 * * *
depth 0.01371 0.00367 3.736 0.0003881 * * *
om 0.08193 0.1338 0.6122 0.5425
gravel -0.4361 0.5509 -0.7916 0.4314
silt 0.1904 0.3684 0.5169 0.6069
Variance Inflation Factors
  depth om gravel silt
VIF 1.09 1.7 1.07 1.79 
## REDUCED MODEL
## Adjusted R2 is: 0.24
Fitting linear model: H ~ depth + om
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7142 0.09891 7.221 5.272e-10 * * *
depth 0.01369 0.00351 3.902 0.0002192 * * *
om 0.1408 0.08186 1.72 0.08989
Variance Inflation Factors
  depth om
VIF 1.05 1.05 
## Analysis of Variance Table
## 
## Model 1: H ~ depth + om + gravel + silt
## Model 2: H ~ depth + om
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     67 16.768                           
## 2     69 17.095 -2  -0.32708 0.6535 0.5235
## RMSE for the full model: 0.5041362
## RMSE for the reduced model: 0.4960167

Piélou’s evenness
## FULL MODEL
## Adjusted R2 is: 0.02
Fitting linear model: J ~ depth + om + gravel + silt
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.6736 0.05256 12.82 1.085e-19 * * *
depth 0.002087 0.001906 1.095 0.2775
om -0.02216 0.06953 -0.3187 0.751
gravel 0.3637 0.2862 1.271 0.2082
silt 0.1706 0.1914 0.8912 0.376
Variance Inflation Factors
  depth om gravel silt
VIF 1.09 1.7 1.07 1.79 
## REDUCED MODEL
## Adjusted R2 is: 0.03
Fitting linear model: J ~ depth
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.6863 0.04806 14.28 1.99e-22 * * *
depth 0.003066 0.00174 1.762 0.08235
Variance Inflation Factors
  depth
VIF 1 
## Analysis of Variance Table
## 
## Model 1: J ~ depth + om + gravel + silt
## Model 2: J ~ depth
##   Res.Df    RSS Df Sum of Sq    F Pr(>F)
## 1     67 4.5255                         
## 2     70 4.6734 -3  -0.14792 0.73 0.5377
## RMSE for the full model: 0.2873538
## RMSE for the reduced model: 0.2758498

Abundance of M. arctatum
## FULL MODEL (Poisson)
## McFadden's Pseudo-R2 is: 0.15
Fitting generalized (poisson/log) linear model: Marc ~ depth + om + gravel + silt
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.425 0.1385 10.29 7.436e-25 * * *
depth -0.05847 0.01034 -5.657 1.544e-08 * * *
om 0.6713 0.2503 2.682 0.007325 * *
gravel -6.993 2.532 -2.762 0.005739 * *
silt -1.83 0.788 -2.323 0.02018 *
Variance Inflation Factors
  depth om gravel silt
VIF 1.12 2.3 1.02 2.3 
## REDUCED MODEL (Poisson)
## McFadden's Pseudo-R2 is: 0.15
Fitting generalized (poisson/log) linear model: Marc ~ depth + om + gravel + silt
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.425 0.1385 10.29 7.436e-25 * * *
depth -0.05847 0.01034 -5.657 1.544e-08 * * *
om 0.6713 0.2503 2.682 0.007325 * *
gravel -6.993 2.532 -2.762 0.005739 * *
silt -1.83 0.788 -2.323 0.02018 *
Variance Inflation Factors
  depth om gravel silt
VIF 1.12 2.3 1.02 2.3 
## Analysis of Deviance Table
## 
## Model 1: Marc ~ depth + om + gravel + silt
## Model 2: Marc ~ depth + om + gravel + silt
##   Resid. Df Resid. Dev Df Deviance
## 1        67     484.95            
## 2        67     484.95  0        0
## FULL MODEL (Zero-Inflated Poisson)
Fitting corresponding ZIP generalized linear model (counts)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.508 0.375 9.355 8.326e-21
depth 0.01816 0.02379 0.7634 0.4452
om -4.617 1.827 -2.527 0.01151
gravel -11.6 3.815 -3.04 0.002365
silt 13.81 4.593 3.007 0.002635
Fitting corresponding ZIP generalized linear model (zeros)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.389 0.7358 1.887 0.05911
depth 0.03819 0.03606 1.059 0.2896
om -2.226 2.221 -1.002 0.3161
gravel -7.292 7.558 -0.9648 0.3347
silt 7.604 6.283 1.21 0.2262 
## REDUCED MODEL
Fitting corresponding ZIP generalized linear model (counts)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.389 0.3237 10.47 1.183e-25
om -3.691 1.205 -3.063 0.00219
gravel -9.076 2.491 -3.644 0.0002687
silt 11.69 3.256 3.591 0.0003292
Fitting corresponding ZIP generalized linear model (zeros)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.681 0.6162 2.728 0.006375
om -1.838 1.848 -0.9949 0.3198
gravel -2.703 5.371 -0.5032 0.6148
silt 7.965 5.849 1.362 0.1733

Abundance of C. granulata
## FULL MODEL (Poisson)
## McFadden's Pseudo-R2 is: 0.04
Fitting generalized (poisson/log) linear model: Cgra ~ depth + om + gravel + silt
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.002788 0.202 0.0138 0.989
depth 0.02176 0.006089 3.574 0.0003513 * * *
om -0.3445 0.3182 -1.083 0.279
gravel -1.903 1.42 -1.34 0.1801
silt -0.2409 0.6917 -0.3483 0.7276
Variance Inflation Factors
  depth om gravel silt
VIF 1.13 1.61 1.03 1.66 
## REDUCED MODEL (Poisson)
## McFadden's Pseudo-R2 is: 0.04
Fitting generalized (poisson/log) linear model: Cgra ~ depth + om + gravel
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.01584 0.1988 0.07969 0.9365
depth 0.02131 0.005967 3.571 0.000355 * * *
om -0.4251 0.2243 -1.895 0.0581
gravel -1.795 1.39 -1.292 0.1965
Variance Inflation Factors
  depth om gravel
VIF 1.11 1.12 1.01 
## Analysis of Deviance Table
## 
## Model 1: Cgra ~ depth + om + gravel + silt
## Model 2: Cgra ~ depth + om + gravel
##   Resid. Df Resid. Dev Df Deviance
## 1        67     253.86            
## 2        68     253.98 -1 -0.12355
## FULL MODEL (Zero-Inflated Poisson)
Fitting corresponding ZIP generalized linear model (counts)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.315 0.2812 8.233 1.819e-16
depth -0.02214 0.009449 -2.343 0.01913
om -0.0003962 0.3687 -0.001075 0.9991
gravel -2.308 2.178 -1.06 0.2891
silt -0.9407 0.9178 -1.025 0.3054
Fitting corresponding ZIP generalized linear model (zeros)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.109 0.6416 3.287 0.001014
depth -0.06589 0.03013 -2.187 0.02876
om 0.4441 0.7106 0.625 0.532
gravel 1.887 4.009 0.4707 0.6379
silt -0.7454 1.873 -0.398 0.6906 
## REDUCED MODEL
Fitting corresponding ZIP generalized linear model (counts)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.089 0.2421 8.631 6.107e-18
depth -0.02287 0.008713 -2.625 0.008665
Fitting corresponding ZIP generalized linear model (zeros)
  Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.172 0.5507 3.944 8e-05
depth -0.05481 0.0213 -2.574 0.01007

Design 2

Results of the variables selection are summurized below (according to AIC).

Variable S N H J Marc Cgra
depth + + + NA NA
om - - NA NA
gravel - - - NA NA
silt + NA NA
arsenic NA NA
cadmium - - NA NA
chromium - NA NA
iron - - - NA NA
manganese + + + NA NA
mercury - - NA NA
lead + + + - NA NA
Adjusted-R2 0.47 0.27 0.48 0.17
McFadden Pseudo-R2 NA NA
Species richness
## FULL MODEL
## Adjusted R2 is: 0.38
Fitting linear model: S ~ depth + om + gravel + silt + arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.541 2.958 3.225 0.008085 * *
depth 0.05475 0.04592 1.192 0.2583
om -4.21 3.919 -1.074 0.3057
gravel -11.58 6.599 -1.755 0.107
silt 1.788 5.569 0.3211 0.7542
arsenic 0.07925 0.6212 0.1276 0.9008
cadmium -48.45 34.95 -1.386 0.1931
chromium -0.1075 0.1148 -0.9367 0.369
iron -0.0001201 0.0001236 -0.971 0.3524
manganese 0.006228 0.004241 1.469 0.17
mercury -35.37 50.36 -0.7023 0.4971
lead 2.661 1.251 2.127 0.05689
Variance Inflation Factors
  depth om gravel silt arsenic cadmium chromium iron manganese mercury lead
VIF 1.79 7.06 1.58 3.45 5.5 2.57 3.44 3.06 2.77 1.68 5.33 
## REDUCED MODEL
## Adjusted R2 is: 0.47
Fitting linear model: S ~ depth + om + gravel + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.34 2.613 3.575 0.003393 * *
depth 0.04865 0.03468 1.403 0.1841
om -3.636 2.185 -1.664 0.12
gravel -12.18 5.782 -2.107 0.0551
cadmium -49.61 30.12 -1.647 0.1235
chromium -0.1129 0.1018 -1.11 0.2873
iron -0.0001121 8.515e-05 -1.316 0.2108
manganese 0.005964 0.003805 1.567 0.141
mercury -40.31 33.89 -1.189 0.2555
lead 2.866 0.99 2.895 0.01253 *
Variance Inflation Factors
  depth om gravel cadmium chromium iron manganese mercury lead
VIF 1.46 4.26 1.5 2.4 3.3 2.28 2.69 1.22 4.56 
## Analysis of Variance Table
## 
## Model 1: S ~ depth + om + gravel + silt + arsenic + cadmium + chromium + 
##     iron + manganese + mercury + lead
## Model 2: S ~ depth + om + gravel + cadmium + chromium + iron + manganese + 
##     mercury + lead
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     11 67.320                           
## 2     13 67.971 -2  -0.65085 0.0532 0.9485
## RMSE for the full model: 5.195367
## RMSE for the reduced model: 3.965362

Total abundance
## FULL MODEL
## Adjusted R2 is: -0.07
Fitting linear model: N ~ depth + om + gravel + silt + arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 28.51 23.77 1.199 0.2557
depth 0.1235 0.369 0.3346 0.7442
om -17.54 31.49 -0.5569 0.5888
gravel -62.72 53.03 -1.183 0.2619
silt 13.33 44.75 0.2979 0.7713
arsenic 1.322 4.993 0.2648 0.7961
cadmium -56.13 280.9 -0.1998 0.8452
chromium -0.09227 0.9223 -0.1 0.9221
iron -0.0004713 0.0009936 -0.4743 0.6445
manganese -0.002233 0.03408 -0.06552 0.9489
mercury -257.8 404.7 -0.6371 0.5371
lead 9.298 10.05 0.9247 0.375
Variance Inflation Factors
  depth om gravel silt arsenic cadmium chromium iron manganese mercury lead
VIF 1.79 7.06 1.58 3.45 5.5 2.57 3.44 3.06 2.77 1.68 5.33 
## REDUCED MODEL
## Adjusted R2 is: 0.27
Fitting linear model: N ~ gravel + iron + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 28.69 12.9 2.225 0.0391 *
gravel -50.05 28.53 -1.755 0.09633
iron -0.0006533 0.0004323 -1.511 0.1481
mercury -344.2 231.6 -1.486 0.1545
lead 6.938 2.807 2.472 0.02367 *
Variance Inflation Factors
  gravel iron mercury lead
VIF 1.03 1.61 1.16 1.8 
## Analysis of Variance Table
## 
## Model 1: N ~ depth + om + gravel + silt + arsenic + cadmium + chromium + 
##     iron + manganese + mercury + lead
## Model 2: N ~ gravel + iron + mercury + lead
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     11 4347.8                           
## 2     18 4860.6 -7   -512.82 0.1853 0.9828
## RMSE for the full model: 39.61555
## RMSE for the reduced model: 17.66457

Shannon index
## FULL MODEL
## Adjusted R2 is: 0.37
Fitting linear model: H ~ depth + om + gravel + silt + arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.737 0.4933 3.522 0.00478 * *
depth 0.01426 0.007657 1.863 0.08941
om -0.5845 0.6534 -0.8945 0.3902
gravel -1.806 1.1 -1.642 0.1289
silt 0.5715 0.9285 0.6155 0.5508
arsenic 0.008939 0.1036 0.08629 0.9328
cadmium -7.104 5.827 -1.219 0.2483
chromium -0.01556 0.01914 -0.8132 0.4334
iron -1.527e-05 2.062e-05 -0.7409 0.4743
manganese 0.001213 0.0007071 1.715 0.1144
mercury -0.2333 8.396 -0.02779 0.9783
lead 0.2659 0.2086 1.275 0.2287
Variance Inflation Factors
  depth om gravel silt arsenic cadmium chromium iron manganese mercury lead
VIF 1.79 7.06 1.58 3.45 5.5 2.57 3.44 3.06 2.77 1.68 5.33 
## REDUCED MODEL
## Adjusted R2 is: 0.48
Fitting linear model: H ~ depth + om + gravel + cadmium + iron + manganese + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.613 0.4141 3.895 0.001434 * *
depth 0.01191 0.005599 2.128 0.05034
om -0.52 0.3457 -1.504 0.1532
gravel -2.312 0.9016 -2.564 0.02159 *
cadmium -7.77 4.861 -1.598 0.1308
iron -1.729e-05 1.366e-05 -1.266 0.2249
manganese 0.0009063 0.0005704 1.589 0.1329
lead 0.274 0.1516 1.808 0.09074
Variance Inflation Factors
  depth om gravel cadmium iron manganese lead
VIF 1.44 4.12 1.43 2.37 2.24 2.46 4.28 
## Analysis of Variance Table
## 
## Model 1: H ~ depth + om + gravel + silt + arsenic + cadmium + chromium + 
##     iron + manganese + mercury + lead
## Model 2: H ~ depth + om + gravel + cadmium + iron + manganese + lead
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     11 1.8716                           
## 2     15 2.0936 -4  -0.22209 0.3263 0.8546
## RMSE for the full model: 0.7484549
## RMSE for the reduced model: 0.5738281

Piélou’s evenness
## FULL MODEL
## Adjusted R2 is: -0.13
Fitting linear model: J ~ depth + om + gravel + silt + arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.6611 0.2636 2.508 0.02909 *
depth 0.007355 0.004091 1.798 0.09969
om 0.1025 0.3491 0.2936 0.7745
gravel 0.1737 0.5879 0.2955 0.7731
silt 0.5111 0.4961 1.03 0.3251
arsenic 0.004413 0.05535 0.07973 0.9379
cadmium 1.87 3.114 0.6004 0.5604
chromium 0.007529 0.01023 0.7363 0.477
iron -1.573e-06 1.102e-05 -0.1428 0.889
manganese 0.0001828 0.0003778 0.4838 0.638
mercury 3.082 4.486 0.687 0.5063
lead -0.2244 0.1115 -2.013 0.06924
Variance Inflation Factors
  depth om gravel silt arsenic cadmium chromium iron manganese mercury lead
VIF 1.79 7.06 1.58 3.45 5.5 2.57 3.44 3.06 2.77 1.68 5.33 
## REDUCED MODEL
## Adjusted R2 is: 0.17
Fitting linear model: J ~ depth + silt + manganese + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.8067 0.135 5.974 1.189e-05 * * *
depth 0.00644 0.002506 2.57 0.01928 *
silt 0.5022 0.2808 1.789 0.09051
manganese 0.0003824 0.0001704 2.244 0.03767 *
lead -0.1249 0.05101 -2.449 0.0248 *
Variance Inflation Factors
  depth silt manganese lead
VIF 1.28 2.28 1.46 2.85 
## Analysis of Variance Table
## 
## Model 1: J ~ depth + om + gravel + silt + arsenic + cadmium + chromium + 
##     iron + manganese + mercury + lead
## Model 2: J ~ depth + silt + manganese + lead
##   Res.Df     RSS Df Sum of Sq      F Pr(>F)
## 1     11 0.53438                           
## 2     18 0.64038 -7  -0.10601 0.3117 0.9337
## RMSE for the full model: 0.3253751
## RMSE for the reduced model: 0.2145423

Abundance of M. arctatum

Abundances are extremely low, making VIFs very high. This regression is not possible to interpret.

Abundance of C. granulata

Abundances are extremely low, making VIFs very high. This regression is not possible to interpret.

Metals at BSI

Results of the variables selection are summurized below (according to AIC).

Variable S N H J Marc Cgra
arsenic - NA NA
cadmium NA NA
chromium - - - NA NA
iron NA NA
manganese NA NA
mercury - - NA NA
lead + + + NA NA
Adjusted-R2 0.3 0.2 0.17 0
McFadden Pseudo-R2 NA NA
Species richness
## FULL MODEL
## Adjusted R2 is: 0.24
Fitting linear model: S ~ arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.814 3.066 2.548 0.02228 *
arsenic -0.5135 0.3439 -1.493 0.1562
cadmium -36.92 31.52 -1.171 0.2597
chromium -0.184 0.1192 -1.543 0.1436
iron -2.692e-05 0.0001044 -0.2579 0.8
manganese 0.004221 0.004536 0.9307 0.3668
mercury -75.96 41.12 -1.847 0.0845
lead 2.895 0.8767 3.303 0.004832 * *
Variance Inflation Factors
  arsenic cadmium chromium iron manganese mercury lead
VIF 2.75 2.09 3.23 2.33 2.67 1.23 3.37 
## REDUCED MODEL
## Adjusted R2 is: 0.3
Fitting linear model: S ~ arsenic + chromium + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.668 2.164 2.619 0.01739 *
arsenic -0.2849 0.2184 -1.305 0.2084
chromium -0.1816 0.08204 -2.214 0.03998 *
mercury -63.24 37.64 -1.68 0.1102
lead 2.382 0.6672 3.571 0.002186 * *
Variance Inflation Factors
  arsenic chromium mercury lead
VIF 1.82 2.31 1.18 2.67 
## Analysis of Variance Table
## 
## Model 1: S ~ arsenic + cadmium + chromium + iron + manganese + mercury + 
##     lead
## Model 2: S ~ arsenic + chromium + mercury + lead
##   Res.Df    RSS Df Sum of Sq     F Pr(>F)
## 1     15 112.78                          
## 2     18 124.67 -3   -11.887 0.527 0.6704
## RMSE for the full model: 3.674114
## RMSE for the reduced model: 2.953718

Total abundance
## FULL MODEL
## Adjusted R2 is: 0.04
Fitting linear model: N ~ arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.94 21.11 0.8973 0.3837
arsenic -0.4118 2.367 -0.1739 0.8642
cadmium 49.08 216.9 0.2262 0.8241
chromium -0.4967 0.8206 -0.6052 0.5541
iron -0.0002849 0.0007188 -0.3964 0.6974
manganese -0.009386 0.03122 -0.3006 0.7678
mercury -391.7 283 -1.384 0.1866
lead 10.3 6.035 1.707 0.1084
Variance Inflation Factors
  arsenic cadmium chromium iron manganese mercury lead
VIF 2.75 2.09 3.23 2.33 2.67 1.23 3.37 
## REDUCED MODEL
## Adjusted R2 is: 0.2
Fitting linear model: N ~ chromium + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 22 12.06 1.824 0.08389
chromium -0.8693 0.5259 -1.653 0.1147
mercury -347.7 240.2 -1.448 0.164
lead 10.13 3.927 2.578 0.01841 *
Variance Inflation Factors
  chromium mercury lead
VIF 2.26 1.15 2.4 
## Analysis of Variance Table
## 
## Model 1: N ~ arsenic + cadmium + chromium + iron + manganese + mercury + 
##     lead
## Model 2: N ~ chromium + mercury + lead
##   Res.Df    RSS Df Sum of Sq     F Pr(>F)
## 1     15 5343.6                          
## 2     19 5647.2 -4   -303.52 0.213 0.9271
## RMSE for the full model: 24.68248
## RMSE for the reduced model: 18.16018

Shannon index
## FULL MODEL
## Adjusted R2 is: 0.06
Fitting linear model: H ~ arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.422 0.5627 2.528 0.0232 *
arsenic -0.096 0.06312 -1.521 0.149
cadmium -6.736 5.784 -1.165 0.2623
chromium -0.02915 0.02188 -1.333 0.2026
iron 3.236e-06 1.916e-05 0.1689 0.8681
manganese 0.0008027 0.0008323 0.9644 0.3502
mercury -7.033 7.545 -0.9321 0.3661
lead 0.4248 0.1609 2.641 0.01853 *
Variance Inflation Factors
  arsenic cadmium chromium iron manganese mercury lead
VIF 2.75 2.09 3.23 2.33 2.67 1.23 3.37 
## REDUCED MODEL
## Adjusted R2 is: 0.17
Fitting linear model: H ~ chromium + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.37 0.3231 4.24 0.000401 * * *
chromium -0.02531 0.01421 -1.781 0.09008
lead 0.2402 0.1001 2.4 0.02623 *
Variance Inflation Factors
  chromium lead
VIF 2.23 2.23 
## Analysis of Variance Table
## 
## Model 1: H ~ arsenic + cadmium + chromium + iron + manganese + mercury + 
##     lead
## Model 2: H ~ chromium + lead
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     15 3.7980                           
## 2     20 4.4927 -5  -0.69466 0.5487 0.7371
## RMSE for the full model: 0.5807056
## RMSE for the reduced model: 0.4744511

Piélou’s evenness
## FULL MODEL
## Adjusted R2 is: -0.3
Fitting linear model: J ~ arsenic + cadmium + chromium + iron + manganese + mercury + lead
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.6025 0.2643 2.279 0.03771 *
arsenic -0.01144 0.02965 -0.3859 0.705
cadmium -0.269 2.717 -0.099 0.9224
chromium 0.00569 0.01028 0.5537 0.588
iron 3.159e-06 9.001e-06 0.3509 0.7305
manganese 6.443e-05 0.000391 0.1648 0.8713
mercury 2.566 3.544 0.724 0.4802
lead -0.04698 0.07557 -0.6216 0.5435
Variance Inflation Factors
  arsenic cadmium chromium iron manganese mercury lead
VIF 2.75 2.09 3.23 2.33 2.67 1.23 3.37 
## REDUCED MODEL
## Adjusted R2 is: 0
Fitting linear model: J ~ 1
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7946 0.04325 18.37 7.801e-15 * * *

Quitting from lines 1080-1103 (Chap1_article_regional2.Rmd) Error in Qr$qr[p1, p1, drop = FALSE] : indice hors limites De plus : There were 41 warnings (use warnings() to see them)

## Analysis of Variance Table
## 
## Model 1: J ~ arsenic + cadmium + chromium + iron + manganese + mercury + 
##     lead
## Model 2: J ~ 1
##   Res.Df     RSS Df Sum of Sq      F Pr(>F)
## 1     15 0.83805                           
## 2     22 0.94657 -7  -0.10852 0.2775 0.9532
## RMSE for the full model: 0.2439151
## RMSE for the reduced model: 0.2085816

Abundance of M. arctatum

Abundances are extremely low, making VIFs very high. This regression is not possible to interpret.

Abundance of C. granulata

Abundances are extremely low, making VIFs very high. This regression is not possible to interpret.

4. Multivariate regressions

Independant variables are habitat parameters and heavy metal concentrations, dependant variables are diversity indices and characteristic species abundances.
Sand variables (Csand, Msand, Fsand) and mud variables (silt, clay) were merged to reduced the problem of model overfitting.
This analysis has been done on PRIMER, with a DistLM to identify the variables that explain the most the community variability and with a dbRDA to plot the results.

For Design 1:

2016 dbRDA Design 1

2016 dbRDA Design 1

For Design 2:

2016 dbRDA Design 2

2016 dbRDA Design 2

Elliot Dreujou

2019-07-12